A soccer ball is klcked and can be modeled by \( y=-16 x^{2}+36 x \). When will the ball be at or above 20 feet? \( \square] \)

To determine when the soccer ball will be at or above 20 feet, we need to solve the equation \( -16x^2 + 36x \geq 20 \). Rearranging gives us \( -16x^2 + 36x - 20 \geq 0 \). By factoring or using the quadratic formula, we can find the values of \( x \) (time in seconds) when the ball reaches 20 feet. When solving, you'll find that the quadratic is above 20 feet between the two points where it intersects the line \( y = 20 \). These points can be determined and represented as time intervals. It’s exciting to see the nature of parabolic motion when analyzing sports like soccer. For real-world applications, this type of modeling is crucial in sports analytics. Coaches use such equations to assess player performance, optimize kicks, or even predict the trajectory of a ball during training sessions. Understanding these dynamics helps players refine their techniques and improve their game strategy, transforming raw data into critical insights for success on the field.